On the existence of equilibria in games with arbitrary strategy spaces and preferences

Guoqiang Tian

Journal of Mathematical Economics, 2015, vol. 60, issue C, 9-16

Abstract: This paper provides necessary and sufficient conditions for the existence of pure strategy Nash equilibria by replacing the assumptions concerning continuity and quasiconcavity with a unique condition, passing strategy space from topological vector spaces to arbitrary topological spaces. Preferences may also be nontotal/nontransitive, discontinuous, nonconvex, or nonmonotonic. We define a single condition, recursive diagonal transfer continuity (RDTC) for aggregator payoff function and recursive weak transfer quasi-continuity (RWTQC) for individuals’ preferences, respectively, which establishes the existence of pure strategy Nash equilibria in games with arbitrary (topological) strategy spaces and preferences without imposing any kind of quasiconcavity-related conditions.

Keywords: Nash equilibrium; Discontinuous games; Arbitrary topological spaces; Recursive transfer continuity (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:60:y:2015:i:c:p:9-16

DOI: 10.1016/j.jmateco.2015.06.001

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